LMFDB - Embedded newform 6790.2.a.bd.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6790,2,Mod(1,6790)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6790, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6790.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6790 = 2 \cdot 5 \cdot 7 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6790.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$54.2184229724$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 33 x^{13} + 62 x^{12} + 417 x^{11} - 720 x^{10} - 2524 x^{9} + 3856 x^{8} + \cdots + 32 $ x^15 - 2x^14 - 33x^13 + 62x^12 + 417x^11 - 720x^10 - 2524x^9 + 3856x^8 + 7452x^7 - 9436x^6 - 9588x^5 + 9160x^4 + 3700x^3 - 3232x^2 + 168x + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.13078$ of defining polynomial
Character	$\chi$	$=$	6790.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.13078 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.13078 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.72134 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.13078 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.13078 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.72134 q^{9} -1.00000 q^{10} -4.86363 q^{11} -1.13078 q^{12} +6.15893 q^{13} +1.00000 q^{14} +1.13078 q^{15} +1.00000 q^{16} -1.53832 q^{17} -1.72134 q^{18} +5.38654 q^{19} -1.00000 q^{20} -1.13078 q^{21} -4.86363 q^{22} +5.36258 q^{23} -1.13078 q^{24} +1.00000 q^{25} +6.15893 q^{26} +5.33879 q^{27} +1.00000 q^{28} +8.25016 q^{29} +1.13078 q^{30} -10.5546 q^{31} +1.00000 q^{32} +5.49970 q^{33} -1.53832 q^{34} -1.00000 q^{35} -1.72134 q^{36} -9.92463 q^{37} +5.38654 q^{38} -6.96440 q^{39} -1.00000 q^{40} -3.37723 q^{41} -1.13078 q^{42} -2.81602 q^{43} -4.86363 q^{44} +1.72134 q^{45} +5.36258 q^{46} -3.00394 q^{47} -1.13078 q^{48} +1.00000 q^{49} +1.00000 q^{50} +1.73950 q^{51} +6.15893 q^{52} -9.46802 q^{53} +5.33879 q^{54} +4.86363 q^{55} +1.00000 q^{56} -6.09100 q^{57} +8.25016 q^{58} +2.41013 q^{59} +1.13078 q^{60} +3.51447 q^{61} -10.5546 q^{62} -1.72134 q^{63} +1.00000 q^{64} -6.15893 q^{65} +5.49970 q^{66} -5.72405 q^{67} -1.53832 q^{68} -6.06390 q^{69} -1.00000 q^{70} +12.5950 q^{71} -1.72134 q^{72} -0.751614 q^{73} -9.92463 q^{74} -1.13078 q^{75} +5.38654 q^{76} -4.86363 q^{77} -6.96440 q^{78} +3.29378 q^{79} -1.00000 q^{80} -0.872994 q^{81} -3.37723 q^{82} +12.1130 q^{83} -1.13078 q^{84} +1.53832 q^{85} -2.81602 q^{86} -9.32912 q^{87} -4.86363 q^{88} -3.56441 q^{89} +1.72134 q^{90} +6.15893 q^{91} +5.36258 q^{92} +11.9349 q^{93} -3.00394 q^{94} -5.38654 q^{95} -1.13078 q^{96} +1.00000 q^{97} +1.00000 q^{98} +8.37194 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} + 2 q^{3} + 15 q^{4} - 15 q^{5} + 2 q^{6} + 15 q^{7} + 15 q^{8} + 25 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 + 2 * q^3 + 15 * q^4 - 15 * q^5 + 2 * q^6 + 15 * q^7 + 15 * q^8 + 25 * q^9	\( 15 q + 15 q^{2} + 2 q^{3} + 15 q^{4} - 15 q^{5} + 2 q^{6} + 15 q^{7} + 15 q^{8} + 25 q^{9} - 15 q^{10} + 13 q^{11} + 2 q^{12} + 3 q^{13} + 15 q^{14} - 2 q^{15} + 15 q^{16} + 11 q^{17} + 25 q^{18} + 4 q^{19} - 15 q^{20} + 2 q^{21} + 13 q^{22} + 21 q^{23} + 2 q^{24} + 15 q^{25} + 3 q^{26} + 8 q^{27} + 15 q^{28} + 18 q^{29} - 2 q^{30} + 4 q^{31} + 15 q^{32} + 5 q^{33} + 11 q^{34} - 15 q^{35} + 25 q^{36} + 16 q^{37} + 4 q^{38} + 12 q^{39} - 15 q^{40} + 3 q^{41} + 2 q^{42} + 17 q^{43} + 13 q^{44} - 25 q^{45} + 21 q^{46} + 4 q^{47} + 2 q^{48} + 15 q^{49} + 15 q^{50} + 17 q^{51} + 3 q^{52} + 30 q^{53} + 8 q^{54} - 13 q^{55} + 15 q^{56} + 10 q^{57} + 18 q^{58} + 10 q^{59} - 2 q^{60} - 5 q^{61} + 4 q^{62} + 25 q^{63} + 15 q^{64} - 3 q^{65} + 5 q^{66} + 25 q^{67} + 11 q^{68} - 26 q^{69} - 15 q^{70} + 44 q^{71} + 25 q^{72} + 11 q^{73} + 16 q^{74} + 2 q^{75} + 4 q^{76} + 13 q^{77} + 12 q^{78} + 3 q^{79} - 15 q^{80} + 63 q^{81} + 3 q^{82} + 4 q^{83} + 2 q^{84} - 11 q^{85} + 17 q^{86} - 6 q^{87} + 13 q^{88} + q^{89} - 25 q^{90} + 3 q^{91} + 21 q^{92} + 16 q^{93} + 4 q^{94} - 4 q^{95} + 2 q^{96} + 15 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 2 * q^3 + 15 * q^4 - 15 * q^5 + 2 * q^6 + 15 * q^7 + 15 * q^8 + 25 * q^9 - 15 * q^10 + 13 * q^11 + 2 * q^12 + 3 * q^13 + 15 * q^14 - 2 * q^15 + 15 * q^16 + 11 * q^17 + 25 * q^18 + 4 * q^19 - 15 * q^20 + 2 * q^21 + 13 * q^22 + 21 * q^23 + 2 * q^24 + 15 * q^25 + 3 * q^26 + 8 * q^27 + 15 * q^28 + 18 * q^29 - 2 * q^30 + 4 * q^31 + 15 * q^32 + 5 * q^33 + 11 * q^34 - 15 * q^35 + 25 * q^36 + 16 * q^37 + 4 * q^38 + 12 * q^39 - 15 * q^40 + 3 * q^41 + 2 * q^42 + 17 * q^43 + 13 * q^44 - 25 * q^45 + 21 * q^46 + 4 * q^47 + 2 * q^48 + 15 * q^49 + 15 * q^50 + 17 * q^51 + 3 * q^52 + 30 * q^53 + 8 * q^54 - 13 * q^55 + 15 * q^56 + 10 * q^57 + 18 * q^58 + 10 * q^59 - 2 * q^60 - 5 * q^61 + 4 * q^62 + 25 * q^63 + 15 * q^64 - 3 * q^65 + 5 * q^66 + 25 * q^67 + 11 * q^68 - 26 * q^69 - 15 * q^70 + 44 * q^71 + 25 * q^72 + 11 * q^73 + 16 * q^74 + 2 * q^75 + 4 * q^76 + 13 * q^77 + 12 * q^78 + 3 * q^79 - 15 * q^80 + 63 * q^81 + 3 * q^82 + 4 * q^83 + 2 * q^84 - 11 * q^85 + 17 * q^86 - 6 * q^87 + 13 * q^88 + q^89 - 25 * q^90 + 3 * q^91 + 21 * q^92 + 16 * q^93 + 4 * q^94 - 4 * q^95 + 2 * q^96 + 15 * q^97 + 15 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.13078	−0.652856	−0.326428	−	0.945222i	$-0.605845\pi$
$3$	−1.13078	−0.652856	−0.326428	+	0.945222i	$0.605845\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.13078	−0.461639
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−1.72134	−0.573779
$10$	−1.00000	−0.316228
$11$	−4.86363	−1.46644	−0.733220	−	0.679992i	$-0.761983\pi$
$11$	−4.86363	−1.46644	−0.733220	+	0.679992i	$0.761983\pi$
$12$	−1.13078	−0.326428
$13$	6.15893	1.70818	0.854090	−	0.520125i	$-0.174115\pi$
$13$	6.15893	1.70818	0.854090	+	0.520125i	$0.174115\pi$
$14$	1.00000	0.267261
$15$	1.13078	0.291966
$16$	1.00000	0.250000
$17$	−1.53832	−0.373097	−0.186548	−	0.982446i	$-0.559730\pi$
$17$	−1.53832	−0.373097	−0.186548	+	0.982446i	$0.559730\pi$
$18$	−1.72134	−0.405723
$19$	5.38654	1.23576	0.617879	−	0.786273i	$-0.287992\pi$
$19$	5.38654	1.23576	0.617879	+	0.786273i	$0.287992\pi$
$20$	−1.00000	−0.223607
$21$	−1.13078	−0.246756
$22$	−4.86363	−1.03693
$23$	5.36258	1.11818	0.559088	−	0.829109i	$-0.311152\pi$
$23$	5.36258	1.11818	0.559088	+	0.829109i	$0.311152\pi$
$24$	−1.13078	−0.230820
$25$	1.00000	0.200000
$26$	6.15893	1.20787
$27$	5.33879	1.02745
$28$	1.00000	0.188982
$29$	8.25016	1.53202	0.766008	−	0.642831i	$-0.222240\pi$
$29$	8.25016	1.53202	0.766008	+	0.642831i	$0.222240\pi$
$30$	1.13078	0.206451
$31$	−10.5546	−1.89566	−0.947831	−	0.318774i	$-0.896729\pi$
$31$	−10.5546	−1.89566	−0.947831	+	0.318774i	$0.896729\pi$
$32$	1.00000	0.176777
$33$	5.49970	0.957374
$34$	−1.53832	−0.263819
$35$	−1.00000	−0.169031
$36$	−1.72134	−0.286889
$37$	−9.92463	−1.63160	−0.815800	−	0.578335i	$-0.803703\pi$
$37$	−9.92463	−1.63160	−0.815800	+	0.578335i	$0.803703\pi$
$38$	5.38654	0.873813
$39$	−6.96440	−1.11520
$40$	−1.00000	−0.158114
$41$	−3.37723	−0.527434	−0.263717	−	0.964600i	$-0.584949\pi$
$41$	−3.37723	−0.527434	−0.263717	+	0.964600i	$0.584949\pi$
$42$	−1.13078	−0.174483
$43$	−2.81602	−0.429438	−0.214719	−	0.976676i	$-0.568884\pi$
$43$	−2.81602	−0.429438	−0.214719	+	0.976676i	$0.568884\pi$
$44$	−4.86363	−0.733220
$45$	1.72134	0.256602
$46$	5.36258	0.790669
$47$	−3.00394	−0.438170	−0.219085	−	0.975706i	$-0.570307\pi$
$47$	−3.00394	−0.438170	−0.219085	+	0.975706i	$0.570307\pi$
$48$	−1.13078	−0.163214
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	1.73950	0.243578
$52$	6.15893	0.854090
$53$	−9.46802	−1.30053	−0.650266	−	0.759706i	$-0.725343\pi$
$53$	−9.46802	−1.30053	−0.650266	+	0.759706i	$0.725343\pi$
$54$	5.33879	0.726518
$55$	4.86363	0.655812
$56$	1.00000	0.133631
$57$	−6.09100	−0.806772
$58$	8.25016	1.08330
$59$	2.41013	0.313772	0.156886	−	0.987617i	$-0.449854\pi$
$59$	2.41013	0.313772	0.156886	+	0.987617i	$0.449854\pi$
$60$	1.13078	0.145983
$61$	3.51447	0.449982	0.224991	−	0.974361i	$-0.427765\pi$
$61$	3.51447	0.449982	0.224991	+	0.974361i	$0.427765\pi$
$62$	−10.5546	−1.34043
$63$	−1.72134	−0.216868
$64$	1.00000	0.125000
$65$	−6.15893	−0.763921
$66$	5.49970	0.676966
$67$	−5.72405	−0.699304	−0.349652	−	0.936880i	$-0.613700\pi$
$67$	−5.72405	−0.699304	−0.349652	+	0.936880i	$0.613700\pi$
$68$	−1.53832	−0.186548
$69$	−6.06390	−0.730008
$70$	−1.00000	−0.119523
$71$	12.5950	1.49475	0.747375	−	0.664403i	$-0.231314\pi$
$71$	12.5950	1.49475	0.747375	+	0.664403i	$0.231314\pi$
$72$	−1.72134	−0.202861
$73$	−0.751614	−0.0879697	−0.0439849	−	0.999032i	$-0.514005\pi$
$73$	−0.751614	−0.0879697	−0.0439849	+	0.999032i	$0.514005\pi$
$74$	−9.92463	−1.15371
$75$	−1.13078	−0.130571
$76$	5.38654	0.617879
$77$	−4.86363	−0.554262
$78$	−6.96440	−0.788563
$79$	3.29378	0.370579	0.185290	−	0.982684i	$-0.440678\pi$
$79$	3.29378	0.370579	0.185290	+	0.982684i	$0.440678\pi$
$80$	−1.00000	−0.111803
$81$	−0.872994	−0.0969994
$82$	−3.37723	−0.372952
$83$	12.1130	1.32957	0.664786	−	0.747034i	$-0.268523\pi$
$83$	12.1130	1.32957	0.664786	+	0.747034i	$0.268523\pi$
$84$	−1.13078	−0.123378
$85$	1.53832	0.166854
$86$	−2.81602	−0.303659
$87$	−9.32912	−1.00019
$88$	−4.86363	−0.518465
$89$	−3.56441	−0.377827	−0.188913	−	0.981994i	$-0.560497\pi$
$89$	−3.56441	−0.377827	−0.188913	+	0.981994i	$0.560497\pi$
$90$	1.72134	0.181445
$91$	6.15893	0.645631
$92$	5.36258	0.559088
$93$	11.9349	1.23759
$94$	−3.00394	−0.309833
$95$	−5.38654	−0.552648
$96$	−1.13078	−0.115410
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	1.00000	0.101015
$99$	8.37194	0.841412
$100$	1.00000	0.100000
$101$	18.8197	1.87263	0.936315	−	0.351162i	$-0.114213\pi$
$101$	18.8197	1.87263	0.936315	+	0.351162i	$0.114213\pi$
$102$	1.73950	0.172236
$103$	−12.7802	−1.25927	−0.629633	−	0.776893i	$-0.716795\pi$
$103$	−12.7802	−1.25927	−0.629633	+	0.776893i	$0.716795\pi$
$104$	6.15893	0.603933
$105$	1.13078	0.110353
$106$	−9.46802	−0.919615
$107$	3.83911	0.371141	0.185570	−	0.982631i	$-0.440587\pi$
$107$	3.83911	0.371141	0.185570	+	0.982631i	$0.440587\pi$
$108$	5.33879	0.513726
$109$	−2.54285	−0.243561	−0.121780	−	0.992557i	$-0.538860\pi$
$109$	−2.54285	−0.243561	−0.121780	+	0.992557i	$0.538860\pi$
$110$	4.86363	0.463729
$111$	11.2226	1.06520
$112$	1.00000	0.0944911
$113$	11.1425	1.04819	0.524097	−	0.851658i	$-0.324403\pi$
$113$	11.1425	1.04819	0.524097	+	0.851658i	$0.324403\pi$
$114$	−6.09100	−0.570474
$115$	−5.36258	−0.500063
$116$	8.25016	0.766008
$117$	−10.6016	−0.980117
$118$	2.41013	0.221870
$119$	−1.53832	−0.141017
$120$	1.13078	0.103226
$121$	12.6549	1.15044
$122$	3.51447	0.318185
$123$	3.81890	0.344339
$124$	−10.5546	−0.947831
$125$	−1.00000	−0.0894427
$126$	−1.72134	−0.153349
$127$	7.71000	0.684152	0.342076	−	0.939672i	$-0.388870\pi$
$127$	7.71000	0.684152	0.342076	+	0.939672i	$0.388870\pi$
$128$	1.00000	0.0883883
$129$	3.18430	0.280362
$130$	−6.15893	−0.540174
$131$	11.4786	1.00289	0.501444	−	0.865190i	$-0.332802\pi$
$131$	11.4786	1.00289	0.501444	+	0.865190i	$0.332802\pi$
$132$	5.49970	0.478687
$133$	5.38654	0.467073
$134$	−5.72405	−0.494483
$135$	−5.33879	−0.459490
$136$	−1.53832	−0.131910
$137$	3.57402	0.305349	0.152675	−	0.988277i	$-0.451211\pi$
$137$	3.57402	0.305349	0.152675	+	0.988277i	$0.451211\pi$
$138$	−6.06390	−0.516193
$139$	21.0541	1.78578	0.892892	−	0.450270i	$-0.148672\pi$
$139$	21.0541	1.78578	0.892892	+	0.450270i	$0.148672\pi$
$140$	−1.00000	−0.0845154
$141$	3.39680	0.286062
$142$	12.5950	1.05695
$143$	−29.9547	−2.50494
$144$	−1.72134	−0.143445
$145$	−8.25016	−0.685138
$146$	−0.751614	−0.0622040
$147$	−1.13078	−0.0932652
$148$	−9.92463	−0.815800
$149$	10.5747	0.866316	0.433158	−	0.901318i	$-0.357399\pi$
$149$	10.5747	0.866316	0.433158	+	0.901318i	$0.357399\pi$
$150$	−1.13078	−0.0923278
$151$	−4.99569	−0.406543	−0.203272	−	0.979122i	$-0.565157\pi$
$151$	−4.99569	−0.406543	−0.203272	+	0.979122i	$0.565157\pi$
$152$	5.38654	0.436906
$153$	2.64796	0.214075
$154$	−4.86363	−0.391922
$155$	10.5546	0.847766
$156$	−6.96440	−0.557598
$157$	−6.49938	−0.518707	−0.259353	−	0.965782i	$-0.583509\pi$
$157$	−6.49938	−0.518707	−0.259353	+	0.965782i	$0.583509\pi$
$158$	3.29378	0.262039
$159$	10.7062	0.849061
$160$	−1.00000	−0.0790569
$161$	5.36258	0.422630
$162$	−0.872994	−0.0685889
$163$	24.0676	1.88512	0.942561	−	0.334034i	$-0.108410\pi$
$163$	24.0676	1.88512	0.942561	+	0.334034i	$0.108410\pi$
$164$	−3.37723	−0.263717
$165$	−5.49970	−0.428151
$166$	12.1130	0.940149
$167$	14.6349	1.13249	0.566243	−	0.824238i	$-0.308396\pi$
$167$	14.6349	1.13249	0.566243	+	0.824238i	$0.308396\pi$
$168$	−1.13078	−0.0872416
$169$	24.9324	1.91788
$170$	1.53832	0.117984
$171$	−9.27205	−0.709052
$172$	−2.81602	−0.214719
$173$	25.0525	1.90470	0.952352	−	0.305001i	$-0.0986569\pi$
$173$	25.0525	1.90470	0.952352	+	0.305001i	$0.0986569\pi$
$174$	−9.32912	−0.707239
$175$	1.00000	0.0755929
$176$	−4.86363	−0.366610
$177$	−2.72533	−0.204848
$178$	−3.56441	−0.267164
$179$	17.8097	1.33116	0.665579	−	0.746328i	$-0.268185\pi$
$179$	17.8097	1.33116	0.665579	+	0.746328i	$0.268185\pi$
$180$	1.72134	0.128301
$181$	−13.3469	−0.992069	−0.496034	−	0.868303i	$-0.665211\pi$
$181$	−13.3469	−0.992069	−0.496034	+	0.868303i	$0.665211\pi$
$182$	6.15893	0.456530
$183$	−3.97410	−0.293774
$184$	5.36258	0.395335
$185$	9.92463	0.729673
$186$	11.9349	0.875111
$187$	7.48180	0.547124
$188$	−3.00394	−0.219085
$189$	5.33879	0.388340
$190$	−5.38654	−0.390781
$191$	24.4322	1.76785	0.883927	−	0.467625i	$-0.154890\pi$
$191$	24.4322	1.76785	0.883927	+	0.467625i	$0.154890\pi$
$192$	−1.13078	−0.0816070
$193$	4.92166	0.354269	0.177135	−	0.984187i	$-0.443317\pi$
$193$	4.92166	0.354269	0.177135	+	0.984187i	$0.443317\pi$
$194$	1.00000	0.0717958
$195$	6.96440	0.498731
$196$	1.00000	0.0714286
$197$	8.52752	0.607561	0.303780	−	0.952742i	$-0.401751\pi$
$197$	8.52752	0.607561	0.303780	+	0.952742i	$0.401751\pi$
$198$	8.37194	0.594968
$199$	14.2077	1.00716	0.503578	−	0.863950i	$-0.332017\pi$
$199$	14.2077	1.00716	0.503578	+	0.863950i	$0.332017\pi$
$200$	1.00000	0.0707107
$201$	6.47264	0.456545
$202$	18.8197	1.32415
$203$	8.25016	0.579048
$204$	1.73950	0.121789
$205$	3.37723	0.235876
$206$	−12.7802	−0.890436
$207$	−9.23080	−0.641585
$208$	6.15893	0.427045
$209$	−26.1982	−1.81216
$210$	1.13078	0.0780313
$211$	−14.7895	−1.01815	−0.509076	−	0.860722i	$-0.670013\pi$
$211$	−14.7895	−1.01815	−0.509076	+	0.860722i	$0.670013\pi$
$212$	−9.46802	−0.650266
$213$	−14.2422	−0.975857
$214$	3.83911	0.262436
$215$	2.81602	0.192051
$216$	5.33879	0.363259
$217$	−10.5546	−0.716493
$218$	−2.54285	−0.172223
$219$	0.849910	0.0574316
$220$	4.86363	0.327906
$221$	−9.47439	−0.637316
$222$	11.2226	0.753210
$223$	3.11679	0.208716	0.104358	−	0.994540i	$-0.466721\pi$
$223$	3.11679	0.208716	0.104358	+	0.994540i	$0.466721\pi$
$224$	1.00000	0.0668153
$225$	−1.72134	−0.114756
$226$	11.1425	0.741186
$227$	−15.8181	−1.04988	−0.524941	−	0.851139i	$-0.675913\pi$
$227$	−15.8181	−1.04988	−0.524941	+	0.851139i	$0.675913\pi$
$228$	−6.09100	−0.403386
$229$	−26.0476	−1.72127	−0.860636	−	0.509221i	$-0.829934\pi$
$229$	−26.0476	−1.72127	−0.860636	+	0.509221i	$0.829934\pi$
$230$	−5.36258	−0.353598
$231$	5.49970	0.361853
$232$	8.25016	0.541649
$233$	−19.0326	−1.24687	−0.623433	−	0.781877i	$-0.714263\pi$
$233$	−19.0326	−1.24687	−0.623433	+	0.781877i	$0.714263\pi$
$234$	−10.6016	−0.693047
$235$	3.00394	0.195956
$236$	2.41013	0.156886
$237$	−3.72454	−0.241935
$238$	−1.53832	−0.0997143
$239$	0.157681	0.0101996	0.00509978	−	0.999987i	$-0.498377\pi$
$239$	0.157681	0.0101996	0.00509978	+	0.999987i	$0.498377\pi$
$240$	1.13078	0.0729916
$241$	3.73674	0.240705	0.120352	−	0.992731i	$-0.461598\pi$
$241$	3.73674	0.240705	0.120352	+	0.992731i	$0.461598\pi$
$242$	12.6549	0.813487
$243$	−15.0292	−0.964125
$244$	3.51447	0.224991
$245$	−1.00000	−0.0638877
$246$	3.81890	0.243484
$247$	33.1753	2.11090
$248$	−10.5546	−0.670217
$249$	−13.6971	−0.868019
$250$	−1.00000	−0.0632456
$251$	−24.9546	−1.57512	−0.787560	−	0.616239i	$-0.788656\pi$
$251$	−24.9546	−1.57512	−0.787560	+	0.616239i	$0.788656\pi$
$252$	−1.72134	−0.108434
$253$	−26.0816	−1.63974
$254$	7.71000	0.483769
$255$	−1.73950	−0.108932
$256$	1.00000	0.0625000
$257$	−2.24458	−0.140013	−0.0700065	−	0.997547i	$-0.522302\pi$
$257$	−2.24458	−0.140013	−0.0700065	+	0.997547i	$0.522302\pi$
$258$	3.18430	0.198246
$259$	−9.92463	−0.616687
$260$	−6.15893	−0.381961
$261$	−14.2013	−0.879038
$262$	11.4786	0.709149
$263$	27.0819	1.66994	0.834971	−	0.550293i	$-0.185484\pi$
$263$	27.0819	1.66994	0.834971	+	0.550293i	$0.185484\pi$
$264$	5.49970	0.338483
$265$	9.46802	0.581616
$266$	5.38654	0.330270
$267$	4.03057	0.246667
$268$	−5.72405	−0.349652
$269$	12.7633	0.778194	0.389097	−	0.921197i	$-0.372787\pi$
$269$	12.7633	0.778194	0.389097	+	0.921197i	$0.372787\pi$
$270$	−5.33879	−0.324909
$271$	6.39436	0.388429	0.194215	−	0.980959i	$-0.437784\pi$
$271$	6.39436	0.388429	0.194215	+	0.980959i	$0.437784\pi$
$272$	−1.53832	−0.0932742
$273$	−6.96440	−0.421504
$274$	3.57402	0.215915
$275$	−4.86363	−0.293288
$276$	−6.06390	−0.365004
$277$	27.1808	1.63314	0.816569	−	0.577248i	$-0.195874\pi$
$277$	27.1808	1.63314	0.816569	+	0.577248i	$0.195874\pi$
$278$	21.0541	1.26274
$279$	18.1680	1.08769
$280$	−1.00000	−0.0597614
$281$	−0.577497	−0.0344506	−0.0172253	−	0.999852i	$-0.505483\pi$
$281$	−0.577497	−0.0344506	−0.0172253	+	0.999852i	$0.505483\pi$
$282$	3.39680	0.202277
$283$	4.49189	0.267015	0.133508	−	0.991048i	$-0.457376\pi$
$283$	4.49189	0.267015	0.133508	+	0.991048i	$0.457376\pi$
$284$	12.5950	0.747375
$285$	6.09100	0.360800
$286$	−29.9547	−1.77126
$287$	−3.37723	−0.199351
$288$	−1.72134	−0.101431
$289$	−14.6336	−0.860799
$290$	−8.25016	−0.484466
$291$	−1.13078	−0.0662875
$292$	−0.751614	−0.0439849
$293$	16.1354	0.942642	0.471321	−	0.881962i	$-0.343777\pi$
$293$	16.1354	0.942642	0.471321	+	0.881962i	$0.343777\pi$
$294$	−1.13078	−0.0659484
$295$	−2.41013	−0.140323
$296$	−9.92463	−0.576857
$297$	−25.9659	−1.50669
$298$	10.5747	0.612578
$299$	33.0277	1.91004
$300$	−1.13078	−0.0652856
$301$	−2.81602	−0.162312
$302$	−4.99569	−0.287469
$303$	−21.2809	−1.22256
$304$	5.38654	0.308939
$305$	−3.51447	−0.201238
$306$	2.64796	0.151374
$307$	−18.1933	−1.03834	−0.519172	−	0.854670i	$-0.673760\pi$
$307$	−18.1933	−1.03834	−0.519172	+	0.854670i	$0.673760\pi$
$308$	−4.86363	−0.277131
$309$	14.4516	0.822120
$310$	10.5546	0.599461
$311$	−28.5194	−1.61719	−0.808594	−	0.588367i	$-0.799771\pi$
$311$	−28.5194	−1.61719	−0.808594	+	0.588367i	$0.799771\pi$
$312$	−6.96440	−0.394281
$313$	−19.7127	−1.11423	−0.557115	−	0.830436i	$-0.688092\pi$
$313$	−19.7127	−1.11423	−0.557115	+	0.830436i	$0.688092\pi$
$314$	−6.49938	−0.366781
$315$	1.72134	0.0969863
$316$	3.29378	0.185290
$317$	15.4918	0.870107	0.435054	−	0.900405i	$-0.356729\pi$
$317$	15.4918	0.870107	0.435054	+	0.900405i	$0.356729\pi$
$318$	10.7062	0.600377
$319$	−40.1257	−2.24661
$320$	−1.00000	−0.0559017
$321$	−4.34119	−0.242302
$322$	5.36258	0.298845
$323$	−8.28621	−0.461057
$324$	−0.872994	−0.0484997
$325$	6.15893	0.341636
$326$	24.0676	1.33298
$327$	2.87540	0.159010
$328$	−3.37723	−0.186476
$329$	−3.00394	−0.165613
$330$	−5.49970	−0.302748
$331$	9.16330	0.503661	0.251830	−	0.967771i	$-0.418968\pi$
$331$	9.16330	0.503661	0.251830	+	0.967771i	$0.418968\pi$
$332$	12.1130	0.664786
$333$	17.0836	0.936177
$334$	14.6349	0.800788
$335$	5.72405	0.312738
$336$	−1.13078	−0.0616891
$337$	23.7147	1.29182	0.645912	−	0.763412i	$-0.276477\pi$
$337$	23.7147	1.29182	0.645912	+	0.763412i	$0.276477\pi$
$338$	24.9324	1.35614
$339$	−12.5997	−0.684321
$340$	1.53832	0.0834269
$341$	51.3336	2.77987
$342$	−9.27205	−0.501375
$343$	1.00000	0.0539949
$344$	−2.81602	−0.151829
$345$	6.06390	0.326469
$346$	25.0525	1.34683
$347$	24.0253	1.28975	0.644874	−	0.764289i	$-0.276910\pi$
$347$	24.0253	1.28975	0.644874	+	0.764289i	$0.276910\pi$
$348$	−9.32912	−0.500093
$349$	−32.0372	−1.71491	−0.857456	−	0.514558i	$-0.827956\pi$
$349$	−32.0372	−1.71491	−0.857456	+	0.514558i	$0.827956\pi$
$350$	1.00000	0.0534522
$351$	32.8813	1.75507
$352$	−4.86363	−0.259232
$353$	1.68427	0.0896447	0.0448224	−	0.998995i	$-0.485728\pi$
$353$	1.68427	0.0896447	0.0448224	+	0.998995i	$0.485728\pi$
$354$	−2.72533	−0.144849
$355$	−12.5950	−0.668472
$356$	−3.56441	−0.188913
$357$	1.73950	0.0920640
$358$	17.8097	0.941270
$359$	−28.7714	−1.51849	−0.759247	−	0.650802i	$-0.774433\pi$
$359$	−28.7714	−1.51849	−0.759247	+	0.650802i	$0.774433\pi$
$360$	1.72134	0.0907224
$361$	10.0149	0.527098
$362$	−13.3469	−0.701499
$363$	−14.3099	−0.751075
$364$	6.15893	0.322816
$365$	0.751614	0.0393413
$366$	−3.97410	−0.207729
$367$	−0.939957	−0.0490654	−0.0245327	−	0.999699i	$-0.507810\pi$
$367$	−0.939957	−0.0490654	−0.0245327	+	0.999699i	$0.507810\pi$
$368$	5.36258	0.279544
$369$	5.81334	0.302631
$370$	9.92463	0.515957
$371$	−9.46802	−0.491555
$372$	11.9349	0.618797
$373$	−8.05993	−0.417327	−0.208664	−	0.977987i	$-0.566911\pi$
$373$	−8.05993	−0.417327	−0.208664	+	0.977987i	$0.566911\pi$
$374$	7.48180	0.386875
$375$	1.13078	0.0583932
$376$	−3.00394	−0.154917
$377$	50.8122	2.61696
$378$	5.33879	0.274598
$379$	6.95153	0.357076	0.178538	−	0.983933i	$-0.442863\pi$
$379$	6.95153	0.357076	0.178538	+	0.983933i	$0.442863\pi$
$380$	−5.38654	−0.276324
$381$	−8.71832	−0.446653
$382$	24.4322	1.25006
$383$	−20.4833	−1.04665	−0.523325	−	0.852133i	$-0.675309\pi$
$383$	−20.4833	−1.04665	−0.523325	+	0.852133i	$0.675309\pi$
$384$	−1.13078	−0.0577049
$385$	4.86363	0.247873
$386$	4.92166	0.250506
$387$	4.84731	0.246403
$388$	1.00000	0.0507673
$389$	−6.95100	−0.352430	−0.176215	−	0.984352i	$-0.556385\pi$
$389$	−6.95100	−0.352430	−0.176215	+	0.984352i	$0.556385\pi$
$390$	6.96440	0.352656
$391$	−8.24935	−0.417187
$392$	1.00000	0.0505076
$393$	−12.9798	−0.654742
$394$	8.52752	0.429610
$395$	−3.29378	−0.165728
$396$	8.37194	0.420706
$397$	−10.8058	−0.542328	−0.271164	−	0.962533i	$-0.587409\pi$
$397$	−10.8058	−0.542328	−0.271164	+	0.962533i	$0.587409\pi$
$398$	14.2077	0.712167
$399$	−6.09100	−0.304931
$400$	1.00000	0.0500000
$401$	9.46504	0.472662	0.236331	−	0.971673i	$-0.424055\pi$
$401$	9.46504	0.472662	0.236331	+	0.971673i	$0.424055\pi$
$402$	6.47264	0.322826
$403$	−65.0050	−3.23813
$404$	18.8197	0.936315
$405$	0.872994	0.0433794
$406$	8.25016	0.409449
$407$	48.2697	2.39264
$408$	1.73950	0.0861180
$409$	−2.48710	−0.122979	−0.0614895	−	0.998108i	$-0.519585\pi$
$409$	−2.48710	−0.122979	−0.0614895	+	0.998108i	$0.519585\pi$
$410$	3.37723	0.166789
$411$	−4.04143	−0.199349
$412$	−12.7802	−0.629633
$413$	2.41013	0.118595
$414$	−9.23080	−0.453669
$415$	−12.1130	−0.594602
$416$	6.15893	0.301966
$417$	−23.8076	−1.16586
$418$	−26.1982	−1.28139
$419$	23.1840	1.13261	0.566307	−	0.824194i	$-0.308372\pi$
$419$	23.1840	1.13261	0.566307	+	0.824194i	$0.308372\pi$
$420$	1.13078	0.0551764
$421$	−21.4312	−1.04449	−0.522247	−	0.852794i	$-0.674906\pi$
$421$	−21.4312	−1.04449	−0.522247	+	0.852794i	$0.674906\pi$
$422$	−14.7895	−0.719942
$423$	5.17080	0.251413
$424$	−9.46802	−0.459808
$425$	−1.53832	−0.0746193
$426$	−14.2422	−0.690035
$427$	3.51447	0.170077
$428$	3.83911	0.185570
$429$	33.8722	1.63537
$430$	2.81602	0.135800
$431$	23.9475	1.15351	0.576755	−	0.816917i	$-0.304319\pi$
$431$	23.9475	1.15351	0.576755	+	0.816917i	$0.304319\pi$
$432$	5.33879	0.256863
$433$	−13.2605	−0.637261	−0.318631	−	0.947879i	$-0.603223\pi$
$433$	−13.2605	−0.637261	−0.318631	+	0.947879i	$0.603223\pi$
$434$	−10.5546	−0.506637
$435$	9.32912	0.447297
$436$	−2.54285	−0.121780
$437$	28.8858	1.38179
$438$	0.849910	0.0406103
$439$	26.5980	1.26945	0.634726	−	0.772737i	$-0.281113\pi$
$439$	26.5980	1.26945	0.634726	+	0.772737i	$0.281113\pi$
$440$	4.86363	0.231864
$441$	−1.72134	−0.0819684
$442$	−9.47439	−0.450651
$443$	−8.37633	−0.397971	−0.198986	−	0.980002i	$-0.563765\pi$
$443$	−8.37633	−0.397971	−0.198986	+	0.980002i	$0.563765\pi$
$444$	11.2226	0.532600
$445$	3.56441	0.168969
$446$	3.11679	0.147584
$447$	−11.9577	−0.565580
$448$	1.00000	0.0472456
$449$	−9.06202	−0.427663	−0.213831	−	0.976871i	$-0.568594\pi$
$449$	−9.06202	−0.427663	−0.213831	+	0.976871i	$0.568594\pi$
$450$	−1.72134	−0.0811446
$451$	16.4256	0.773450
$452$	11.1425	0.524097
$453$	5.64902	0.265414
$454$	−15.8181	−0.742379
$455$	−6.15893	−0.288735
$456$	−6.09100	−0.285237
$457$	2.49616	0.116766	0.0583828	−	0.998294i	$-0.481406\pi$
$457$	2.49616	0.116766	0.0583828	+	0.998294i	$0.481406\pi$
$458$	−26.0476	−1.21712
$459$	−8.21276	−0.383339
$460$	−5.36258	−0.250032
$461$	−20.7975	−0.968636	−0.484318	−	0.874892i	$-0.660932\pi$
$461$	−20.7975	−0.968636	−0.484318	+	0.874892i	$0.660932\pi$
$462$	5.49970	0.255869
$463$	7.64339	0.355218	0.177609	−	0.984101i	$-0.443164\pi$
$463$	7.64339	0.355218	0.177609	+	0.984101i	$0.443164\pi$
$464$	8.25016	0.383004
$465$	−11.9349	−0.553469
$466$	−19.0326	−0.881668
$467$	−11.6185	−0.537639	−0.268819	−	0.963191i	$-0.586634\pi$
$467$	−11.6185	−0.537639	−0.268819	+	0.963191i	$0.586634\pi$
$468$	−10.6016	−0.490059
$469$	−5.72405	−0.264312
$470$	3.00394	0.138562
$471$	7.34937	0.338641
$472$	2.41013	0.110935
$473$	13.6961	0.629745
$474$	−3.72454	−0.171074
$475$	5.38654	0.247152
$476$	−1.53832	−0.0705086
$477$	16.2976	0.746218
$478$	0.157681	0.00721217
$479$	19.9474	0.911422	0.455711	−	0.890128i	$-0.349385\pi$
$479$	19.9474	0.911422	0.455711	+	0.890128i	$0.349385\pi$
$480$	1.13078	0.0516128
$481$	−61.1251	−2.78707
$482$	3.73674	0.170204
$483$	−6.06390	−0.275917
$484$	12.6549	0.575222
$485$	−1.00000	−0.0454077
$486$	−15.0292	−0.681739
$487$	11.9989	0.543721	0.271861	−	0.962337i	$-0.412361\pi$
$487$	11.9989	0.543721	0.271861	+	0.962337i	$0.412361\pi$
$488$	3.51447	0.159093
$489$	−27.2152	−1.23071
$490$	−1.00000	−0.0451754
$491$	22.1958	1.00168	0.500842	−	0.865539i	$-0.333024\pi$
$491$	22.1958	1.00168	0.500842	+	0.865539i	$0.333024\pi$
$492$	3.81890	0.172169
$493$	−12.6914	−0.571590
$494$	33.1753	1.49263
$495$	−8.37194	−0.376291
$496$	−10.5546	−0.473915
$497$	12.5950	0.564962
$498$	−13.6971	−0.613782
$499$	−14.8988	−0.666960	−0.333480	−	0.942757i	$-0.608223\pi$
$499$	−14.8988	−0.666960	−0.333480	+	0.942757i	$0.608223\pi$
$500$	−1.00000	−0.0447214
$501$	−16.5489	−0.739350
$502$	−24.9546	−1.11378
$503$	−29.1192	−1.29836	−0.649181	−	0.760634i	$-0.724888\pi$
$503$	−29.1192	−1.29836	−0.649181	+	0.760634i	$0.724888\pi$
$504$	−1.72134	−0.0766744
$505$	−18.8197	−0.837465
$506$	−26.0816	−1.15947
$507$	−28.1931	−1.25210
$508$	7.71000	0.342076
$509$	4.21108	0.186653	0.0933265	−	0.995636i	$-0.470250\pi$
$509$	4.21108	0.186653	0.0933265	+	0.995636i	$0.470250\pi$
$510$	−1.73950	−0.0770263
$511$	−0.751614	−0.0332494
$512$	1.00000	0.0441942
$513$	28.7576	1.26968
$514$	−2.24458	−0.0990041
$515$	12.7802	0.563161
$516$	3.18430	0.140181
$517$	14.6101	0.642550
$518$	−9.92463	−0.436063
$519$	−28.3288	−1.24350
$520$	−6.15893	−0.270087
$521$	35.4598	1.55352	0.776760	−	0.629797i	$-0.216862\pi$
$521$	35.4598	1.55352	0.776760	+	0.629797i	$0.216862\pi$
$522$	−14.2013	−0.621574
$523$	−15.7166	−0.687239	−0.343620	−	0.939109i	$-0.611653\pi$
$523$	−15.7166	−0.687239	−0.343620	+	0.939109i	$0.611653\pi$
$524$	11.4786	0.501444
$525$	−1.13078	−0.0493513
$526$	27.0819	1.18083
$527$	16.2363	0.707265
$528$	5.49970	0.239344
$529$	5.75725	0.250315
$530$	9.46802	0.411264
$531$	−4.14864	−0.180036
$532$	5.38654	0.233536
$533$	−20.8001	−0.900953
$534$	4.03057	0.174420
$535$	−3.83911	−0.165979
$536$	−5.72405	−0.247241
$537$	−20.1388	−0.869054
$538$	12.7633	0.550266
$539$	−4.86363	−0.209491
$540$	−5.33879	−0.229745
$541$	−12.2348	−0.526015	−0.263008	−	0.964794i	$-0.584714\pi$
$541$	−12.2348	−0.526015	−0.263008	+	0.964794i	$0.584714\pi$
$542$	6.39436	0.274661
$543$	15.0924	0.647678
$544$	−1.53832	−0.0659548
$545$	2.54285	0.108924
$546$	−6.96440	−0.298049
$547$	−28.7806	−1.23057	−0.615286	−	0.788304i	$-0.710959\pi$
$547$	−28.7806	−1.23057	−0.615286	+	0.788304i	$0.710959\pi$
$548$	3.57402	0.152675
$549$	−6.04959	−0.258190
$550$	−4.86363	−0.207386
$551$	44.4398	1.89320
$552$	−6.06390	−0.258097
$553$	3.29378	0.140066
$554$	27.1808	1.15480
$555$	−11.2226	−0.476372
$556$	21.0541	0.892892
$557$	1.46427	0.0620431	0.0310215	−	0.999519i	$-0.490124\pi$
$557$	1.46427	0.0620431	0.0310215	+	0.999519i	$0.490124\pi$
$558$	18.1680	0.769113
$559$	−17.3436	−0.733558
$560$	−1.00000	−0.0422577
$561$	−8.46027	−0.357193
$562$	−0.577497	−0.0243603
$563$	−24.7307	−1.04228	−0.521138	−	0.853472i	$-0.674492\pi$
$563$	−24.7307	−1.04228	−0.521138	+	0.853472i	$0.674492\pi$
$564$	3.39680	0.143031
$565$	−11.1425	−0.468767
$566$	4.49189	0.188808
$567$	−0.872994	−0.0366623
$568$	12.5950	0.528474
$569$	17.4974	0.733530	0.366765	−	0.930314i	$-0.380465\pi$
$569$	17.4974	0.733530	0.366765	+	0.930314i	$0.380465\pi$
$570$	6.09100	0.255124
$571$	11.3255	0.473958	0.236979	−	0.971515i	$-0.423843\pi$
$571$	11.3255	0.473958	0.236979	+	0.971515i	$0.423843\pi$
$572$	−29.9547	−1.25247
$573$	−27.6275	−1.15415
$574$	−3.37723	−0.140963
$575$	5.36258	0.223635
$576$	−1.72134	−0.0717223
$577$	−9.81032	−0.408409	−0.204204	−	0.978928i	$-0.565461\pi$
$577$	−9.81032	−0.408409	−0.204204	+	0.978928i	$0.565461\pi$
$578$	−14.6336	−0.608677
$579$	−5.56532	−0.231287
$580$	−8.25016	−0.342569
$581$	12.1130	0.502531
$582$	−1.13078	−0.0468724
$583$	46.0489	1.90715
$584$	−0.751614	−0.0311020
$585$	10.6016	0.438322
$586$	16.1354	0.666548
$587$	21.2724	0.878005	0.439003	−	0.898486i	$-0.355332\pi$
$587$	21.2724	0.878005	0.439003	+	0.898486i	$0.355332\pi$
$588$	−1.13078	−0.0466326
$589$	−56.8528	−2.34258
$590$	−2.41013	−0.0992234
$591$	−9.64276	−0.396650
$592$	−9.92463	−0.407900
$593$	40.4519	1.66116	0.830581	−	0.556898i	$-0.188009\pi$
$593$	40.4519	1.66116	0.830581	+	0.556898i	$0.188009\pi$
$594$	−25.9659	−1.06539
$595$	1.53832	0.0630648
$596$	10.5747	0.433158
$597$	−16.0658	−0.657528
$598$	33.0277	1.35061
$599$	29.2145	1.19367	0.596835	−	0.802364i	$-0.296425\pi$
$599$	29.2145	1.19367	0.596835	+	0.802364i	$0.296425\pi$
$600$	−1.13078	−0.0461639
$601$	11.1503	0.454831	0.227415	−	0.973798i	$-0.426972\pi$
$601$	11.1503	0.454831	0.227415	+	0.973798i	$0.426972\pi$
$602$	−2.81602	−0.114772
$603$	9.85301	0.401246
$604$	−4.99569	−0.203272
$605$	−12.6549	−0.514494
$606$	−21.2809	−0.864479
$607$	29.9097	1.21400	0.606998	−	0.794703i	$-0.292373\pi$
$607$	29.9097	1.21400	0.606998	+	0.794703i	$0.292373\pi$
$608$	5.38654	0.218453
$609$	−9.32912	−0.378035
$610$	−3.51447	−0.142297
$611$	−18.5011	−0.748474
$612$	2.64796	0.107037
$613$	24.4213	0.986368	0.493184	−	0.869925i	$-0.335833\pi$
$613$	24.4213	0.986368	0.493184	+	0.869925i	$0.335833\pi$
$614$	−18.1933	−0.734220
$615$	−3.81890	−0.153993
$616$	−4.86363	−0.195961
$617$	4.40287	0.177253	0.0886264	−	0.996065i	$-0.471752\pi$
$617$	4.40287	0.177253	0.0886264	+	0.996065i	$0.471752\pi$
$618$	14.4516	0.581327
$619$	−13.5823	−0.545917	−0.272959	−	0.962026i	$-0.588002\pi$
$619$	−13.5823	−0.545917	−0.272959	+	0.962026i	$0.588002\pi$
$620$	10.5546	0.423883
$621$	28.6297	1.14887
$622$	−28.5194	−1.14352
$623$	−3.56441	−0.142805
$624$	−6.96440	−0.278799
$625$	1.00000	0.0400000
$626$	−19.7127	−0.787879
$627$	29.6244	1.18308
$628$	−6.49938	−0.259353
$629$	15.2672	0.608744
$630$	1.72134	0.0685797
$631$	−7.66246	−0.305038	−0.152519	−	0.988301i	$-0.548739\pi$
$631$	−7.66246	−0.305038	−0.152519	+	0.988301i	$0.548739\pi$
$632$	3.29378	0.131020
$633$	16.7237	0.664707
$634$	15.4918	0.615259
$635$	−7.71000	−0.305962
$636$	10.7062	0.424530
$637$	6.15893	0.244026
$638$	−40.1257	−1.58859
$639$	−21.6802	−0.857656
$640$	−1.00000	−0.0395285
$641$	−17.2942	−0.683081	−0.341541	−	0.939867i	$-0.610949\pi$
$641$	−17.2942	−0.683081	−0.341541	+	0.939867i	$0.610949\pi$
$642$	−4.34119	−0.171333
$643$	−49.3482	−1.94610	−0.973051	−	0.230590i	$-0.925934\pi$
$643$	−49.3482	−1.94610	−0.973051	+	0.230590i	$0.925934\pi$
$644$	5.36258	0.211315
$645$	−3.18430	−0.125382
$646$	−8.28621	−0.326017
$647$	32.6169	1.28230	0.641152	−	0.767414i	$-0.278457\pi$
$647$	32.6169	1.28230	0.641152	+	0.767414i	$0.278457\pi$
$648$	−0.872994	−0.0342945
$649$	−11.7220	−0.460127
$650$	6.15893	0.241573
$651$	11.9349	0.467767
$652$	24.0676	0.942561
$653$	34.4431	1.34786	0.673931	−	0.738794i	$-0.264604\pi$
$653$	34.4431	1.34786	0.673931	+	0.738794i	$0.264604\pi$
$654$	2.87540	0.112437
$655$	−11.4786	−0.448505
$656$	−3.37723	−0.131859
$657$	1.29378	0.0504752
$658$	−3.00394	−0.117106
$659$	16.1659	0.629732	0.314866	−	0.949136i	$-0.398040\pi$
$659$	16.1659	0.629732	0.314866	+	0.949136i	$0.398040\pi$
$660$	−5.49970	−0.214075
$661$	19.8740	0.773010	0.386505	−	0.922287i	$-0.373682\pi$
$661$	19.8740	0.773010	0.386505	+	0.922287i	$0.373682\pi$
$662$	9.16330	0.356142
$663$	10.7134	0.416076
$664$	12.1130	0.470075
$665$	−5.38654	−0.208881
$666$	17.0836	0.661977
$667$	44.2421	1.71306
$668$	14.6349	0.566243
$669$	−3.52440	−0.136261
$670$	5.72405	0.221139
$671$	−17.0931	−0.659871
$672$	−1.13078	−0.0436208
$673$	−0.999542	−0.0385295	−0.0192648	−	0.999814i	$-0.506133\pi$
$673$	−0.999542	−0.0385295	−0.0192648	+	0.999814i	$0.506133\pi$
$674$	23.7147	0.913457
$675$	5.33879	0.205490
$676$	24.9324	0.958939
$677$	−2.67223	−0.102702	−0.0513511	−	0.998681i	$-0.516353\pi$
$677$	−2.67223	−0.102702	−0.0513511	+	0.998681i	$0.516353\pi$
$678$	−12.5997	−0.483888
$679$	1.00000	0.0383765
$680$	1.53832	0.0589918
$681$	17.8868	0.685422
$682$	51.3336	1.96567
$683$	30.8549	1.18063	0.590314	−	0.807173i	$-0.299004\pi$
$683$	30.8549	1.18063	0.590314	+	0.807173i	$0.299004\pi$
$684$	−9.27205	−0.354526
$685$	−3.57402	−0.136556
$686$	1.00000	0.0381802
$687$	29.4541	1.12374
$688$	−2.81602	−0.107360
$689$	−58.3129	−2.22154
$690$	6.06390	0.230849
$691$	−25.9619	−0.987638	−0.493819	−	0.869565i	$-0.664400\pi$
$691$	−25.9619	−0.987638	−0.493819	+	0.869565i	$0.664400\pi$
$692$	25.0525	0.952352
$693$	8.37194	0.318024
$694$	24.0253	0.911990
$695$	−21.0541	−0.798627
$696$	−9.32912	−0.353619
$697$	5.19525	0.196784
$698$	−32.0372	−1.21263
$699$	21.5217	0.814025
$700$	1.00000	0.0377964
$701$	−4.54318	−0.171593	−0.0857967	−	0.996313i	$-0.527344\pi$
$701$	−4.54318	−0.171593	−0.0857967	+	0.996313i	$0.527344\pi$
$702$	32.8813	1.24102
$703$	−53.4595	−2.01626
$704$	−4.86363	−0.183305
$705$	−3.39680	−0.127931
$706$	1.68427	0.0633884
$707$	18.8197	0.707787
$708$	−2.72533	−0.102424
$709$	−13.2707	−0.498391	−0.249196	−	0.968453i	$-0.580166\pi$
$709$	−13.2707	−0.498391	−0.249196	+	0.968453i	$0.580166\pi$
$710$	−12.5950	−0.472681
$711$	−5.66971	−0.212631
$712$	−3.56441	−0.133582
$713$	−56.5999	−2.11968
$714$	1.73950	0.0650991
$715$	29.9547	1.12024
$716$	17.8097	0.665579
$717$	−0.178303	−0.00665884
$718$	−28.7714	−1.07374
$719$	−1.55381	−0.0579474	−0.0289737	−	0.999580i	$-0.509224\pi$
$719$	−1.55381	−0.0579474	−0.0289737	+	0.999580i	$0.509224\pi$
$720$	1.72134	0.0641504
$721$	−12.7802	−0.475958
$722$	10.0149	0.372714
$723$	−4.22543	−0.157146
$724$	−13.3469	−0.496034
$725$	8.25016	0.306403
$726$	−14.3099	−0.531090
$727$	2.06627	0.0766339	0.0383169	−	0.999266i	$-0.487800\pi$
$727$	2.06627	0.0766339	0.0383169	+	0.999266i	$0.487800\pi$
$728$	6.15893	0.228265
$729$	19.6137	0.726434
$730$	0.751614	0.0278185
$731$	4.33193	0.160222
$732$	−3.97410	−0.146887
$733$	1.15628	0.0427080	0.0213540	−	0.999772i	$-0.493202\pi$
$733$	1.15628	0.0427080	0.0213540	+	0.999772i	$0.493202\pi$
$734$	−0.939957	−0.0346945
$735$	1.13078	0.0417095
$736$	5.36258	0.197667
$737$	27.8397	1.02549
$738$	5.81334	0.213992
$739$	17.0096	0.625709	0.312855	−	0.949801i	$-0.398715\pi$
$739$	17.0096	0.625709	0.312855	+	0.949801i	$0.398715\pi$
$740$	9.92463	0.364837
$741$	−37.5140	−1.37811
$742$	−9.46802	−0.347582
$743$	9.36585	0.343600	0.171800	−	0.985132i	$-0.445042\pi$
$743$	9.36585	0.343600	0.171800	+	0.985132i	$0.445042\pi$
$744$	11.9349	0.437556
$745$	−10.5747	−0.387428
$746$	−8.05993	−0.295095
$747$	−20.8505	−0.762880
$748$	7.48180	0.273562
$749$	3.83911	0.140278
$750$	1.13078	0.0412903
$751$	−3.87415	−0.141370	−0.0706849	−	0.997499i	$-0.522518\pi$
$751$	−3.87415	−0.141370	−0.0706849	+	0.997499i	$0.522518\pi$
$752$	−3.00394	−0.109543
$753$	28.2181	1.02833
$754$	50.8122	1.85047
$755$	4.99569	0.181812
$756$	5.33879	0.194170
$757$	−0.718623	−0.0261188	−0.0130594	−	0.999915i	$-0.504157\pi$
$757$	−0.718623	−0.0261188	−0.0130594	+	0.999915i	$0.504157\pi$
$758$	6.95153	0.252491
$759$	29.4926	1.07051
$760$	−5.38654	−0.195390
$761$	−45.1270	−1.63585	−0.817927	−	0.575322i	$-0.804877\pi$
$761$	−45.1270	−1.63585	−0.817927	+	0.575322i	$0.804877\pi$
$762$	−8.71832	−0.315831
$763$	−2.54285	−0.0920573
$764$	24.4322	0.883927
$765$	−2.64796	−0.0957372
$766$	−20.4833	−0.740093
$767$	14.8438	0.535979
$768$	−1.13078	−0.0408035
$769$	−31.6293	−1.14058	−0.570291	−	0.821443i	$-0.693170\pi$
$769$	−31.6293	−1.14058	−0.570291	+	0.821443i	$0.693170\pi$
$770$	4.86363	0.175273
$771$	2.53812	0.0914083
$772$	4.92166	0.177135
$773$	30.9964	1.11486	0.557431	−	0.830223i	$-0.311787\pi$
$773$	30.9964	1.11486	0.557431	+	0.830223i	$0.311787\pi$
$774$	4.84731	0.174233
$775$	−10.5546	−0.379132
$776$	1.00000	0.0358979
$777$	11.2226	0.402608
$778$	−6.95100	−0.249206
$779$	−18.1916	−0.651781
$780$	6.96440	0.249365
$781$	−61.2573	−2.19196
$782$	−8.24935	−0.294996
$783$	44.0459	1.57407
$784$	1.00000	0.0357143
$785$	6.49938	0.231973
$786$	−12.9798	−0.462972
$787$	52.1521	1.85902	0.929511	−	0.368796i	$-0.120230\pi$
$787$	52.1521	1.85902	0.929511	+	0.368796i	$0.120230\pi$
$788$	8.52752	0.303780
$789$	−30.6237	−1.09023
$790$	−3.29378	−0.117188
$791$	11.1425	0.396180
$792$	8.37194	0.297484
$793$	21.6454	0.768650
$794$	−10.8058	−0.383484
$795$	−10.7062	−0.379712
$796$	14.2077	0.503578
$797$	19.9701	0.707378	0.353689	−	0.935363i	$-0.384927\pi$
$797$	19.9701	0.707378	0.353689	+	0.935363i	$0.384927\pi$
$798$	−6.09100	−0.215619
$799$	4.62102	0.163480
$800$	1.00000	0.0353553
$801$	6.13555	0.216789
$802$	9.46504	0.334222
$803$	3.65557	0.129002
$804$	6.47264	0.228272
$805$	−5.36258	−0.189006
$806$	−65.0050	−2.28970
$807$	−14.4325	−0.508049
$808$	18.8197	0.662074
$809$	−31.6083	−1.11129	−0.555643	−	0.831421i	$-0.687528\pi$
$809$	−31.6083	−1.11129	−0.555643	+	0.831421i	$0.687528\pi$
$810$	0.872994	0.0306739
$811$	46.9980	1.65032	0.825161	−	0.564898i	$-0.191085\pi$
$811$	46.9980	1.65032	0.825161	+	0.564898i	$0.191085\pi$
$812$	8.25016	0.289524
$813$	−7.23061	−0.253589
$814$	48.2697	1.69185
$815$	−24.0676	−0.843052
$816$	1.73950	0.0608946
$817$	−15.1686	−0.530682
$818$	−2.48710	−0.0869593
$819$	−10.6016	−0.370449
$820$	3.37723	0.117938
$821$	−28.8599	−1.00722	−0.503609	−	0.863932i	$-0.667995\pi$
$821$	−28.8599	−1.00722	−0.503609	+	0.863932i	$0.667995\pi$
$822$	−4.04143	−0.140961
$823$	−13.0883	−0.456229	−0.228115	−	0.973634i	$-0.573256\pi$
$823$	−13.0883	−0.456229	−0.228115	+	0.973634i	$0.573256\pi$
$824$	−12.7802	−0.445218
$825$	5.49970	0.191475
$826$	2.41013	0.0838591
$827$	15.4815	0.538346	0.269173	−	0.963092i	$-0.413250\pi$
$827$	15.4815	0.538346	0.269173	+	0.963092i	$0.413250\pi$
$828$	−9.23080	−0.320792
$829$	−40.3040	−1.39982	−0.699908	−	0.714233i	$-0.746776\pi$
$829$	−40.3040	−1.39982	−0.699908	+	0.714233i	$0.746776\pi$
$830$	−12.1130	−0.420447
$831$	−30.7355	−1.06620
$832$	6.15893	0.213522
$833$	−1.53832	−0.0532995
$834$	−23.8076	−0.824388
$835$	−14.6349	−0.506463
$836$	−26.1982	−0.906082
$837$	−56.3488	−1.94770
$838$	23.1840	0.800879
$839$	−7.11690	−0.245703	−0.122851	−	0.992425i	$-0.539204\pi$
$839$	−7.11690	−0.245703	−0.122851	+	0.992425i	$0.539204\pi$
$840$	1.13078	0.0390156
$841$	39.0651	1.34707
$842$	−21.4312	−0.738569
$843$	0.653023	0.0224913
$844$	−14.7895	−0.509076
$845$	−24.9324	−0.857701
$846$	5.17080	0.177776
$847$	12.6549	0.434827
$848$	−9.46802	−0.325133
$849$	−5.07934	−0.174323
$850$	−1.53832	−0.0527638
$851$	−53.2216	−1.82441
$852$	−14.2422	−0.487928
$853$	−40.5940	−1.38991	−0.694956	−	0.719053i	$-0.744576\pi$
$853$	−40.5940	−1.38991	−0.694956	+	0.719053i	$0.744576\pi$
$854$	3.51447	0.120263
$855$	9.27205	0.317097
$856$	3.83911	0.131218
$857$	−6.16317	−0.210530	−0.105265	−	0.994444i	$-0.533569\pi$
$857$	−6.16317	−0.210530	−0.105265	+	0.994444i	$0.533569\pi$
$858$	33.8722	1.15638
$859$	−42.6760	−1.45609	−0.728044	−	0.685531i	$-0.759570\pi$
$859$	−42.6760	−1.45609	−0.728044	+	0.685531i	$0.759570\pi$
$860$	2.81602	0.0960254
$861$	3.81890	0.130148
$862$	23.9475	0.815655
$863$	−29.5793	−1.00689	−0.503446	−	0.864027i	$-0.667935\pi$
$863$	−29.5793	−1.00689	−0.503446	+	0.864027i	$0.667935\pi$
$864$	5.33879	0.181629
$865$	−25.0525	−0.851809
$866$	−13.2605	−0.450612
$867$	16.5474	0.561978
$868$	−10.5546	−0.358246
$869$	−16.0197	−0.543432
$870$	9.32912	0.316287
$871$	−35.2540	−1.19454
$872$	−2.54285	−0.0861117
$873$	−1.72134	−0.0582584
$874$	28.8858	0.977076
$875$	−1.00000	−0.0338062
$876$	0.849910	0.0287158
$877$	57.2857	1.93440	0.967201	−	0.254013i	$-0.0817506\pi$
$877$	57.2857	1.93440	0.967201	+	0.254013i	$0.0817506\pi$
$878$	26.5980	0.897638
$879$	−18.2456	−0.615410
$880$	4.86363	0.163953
$881$	−45.9493	−1.54807	−0.774036	−	0.633142i	$-0.781765\pi$
$881$	−45.9493	−1.54807	−0.774036	+	0.633142i	$0.781765\pi$
$882$	−1.72134	−0.0579604
$883$	33.3619	1.12272	0.561359	−	0.827573i	$-0.310279\pi$
$883$	33.3619	1.12272	0.561359	+	0.827573i	$0.310279\pi$
$884$	−9.47439	−0.318658
$885$	2.72533	0.0916108
$886$	−8.37633	−0.281408
$887$	−2.01692	−0.0677214	−0.0338607	−	0.999427i	$-0.510780\pi$
$887$	−2.01692	−0.0677214	−0.0338607	+	0.999427i	$0.510780\pi$
$888$	11.2226	0.376605
$889$	7.71000	0.258585
$890$	3.56441	0.119479
$891$	4.24592	0.142244
$892$	3.11679	0.104358
$893$	−16.1809	−0.541473
$894$	−11.9577	−0.399925
$895$	−17.8097	−0.595312
$896$	1.00000	0.0334077
$897$	−37.3471	−1.24698
$898$	−9.06202	−0.302403
$899$	−87.0771	−2.90418
$900$	−1.72134	−0.0573779
$901$	14.5648	0.485224
$902$	16.4256	0.546912
$903$	3.18430	0.105967
$904$	11.1425	0.370593
$905$	13.3469	0.443667
$906$	5.64902	0.187676
$907$	49.8538	1.65537	0.827683	−	0.561195i	$-0.189658\pi$
$907$	49.8538	1.65537	0.827683	+	0.561195i	$0.189658\pi$
$908$	−15.8181	−0.524941
$909$	−32.3950	−1.07447
$910$	−6.15893	−0.204167
$911$	21.8695	0.724569	0.362285	−	0.932068i	$-0.381997\pi$
$911$	21.8695	0.724569	0.362285	+	0.932068i	$0.381997\pi$
$912$	−6.09100	−0.201693
$913$	−58.9130	−1.94974
$914$	2.49616	0.0825657
$915$	3.97410	0.131380
$916$	−26.0476	−0.860636
$917$	11.4786	0.379056
$918$	−8.21276	−0.271061
$919$	30.2864	0.999058	0.499529	−	0.866297i	$-0.333506\pi$
$919$	30.2864	0.999058	0.499529	+	0.866297i	$0.333506\pi$
$920$	−5.36258	−0.176799
$921$	20.5726	0.677890
$922$	−20.7975	−0.684929
$923$	77.5716	2.55330
$924$	5.49970	0.180927
$925$	−9.92463	−0.326320
$926$	7.64339	0.251177
$927$	21.9989	0.722540
$928$	8.25016	0.270825
$929$	19.0638	0.625463	0.312732	−	0.949842i	$-0.398756\pi$
$929$	19.0638	0.625463	0.312732	+	0.949842i	$0.398756\pi$
$930$	−11.9349	−0.391362
$931$	5.38654	0.176537
$932$	−19.0326	−0.623433
$933$	32.2492	1.05579
$934$	−11.6185	−0.380168
$935$	−7.48180	−0.244681
$936$	−10.6016	−0.346524
$937$	−0.0795588	−0.00259907	−0.00129954	−	0.999999i	$-0.500414\pi$
$937$	−0.0795588	−0.00259907	−0.00129954	+	0.999999i	$0.500414\pi$
$938$	−5.72405	−0.186897
$939$	22.2908	0.727432
$940$	3.00394	0.0979779
$941$	9.85452	0.321248	0.160624	−	0.987016i	$-0.448649\pi$
$941$	9.85452	0.321248	0.160624	+	0.987016i	$0.448649\pi$
$942$	7.34937	0.239455
$943$	−18.1106	−0.589764
$944$	2.41013	0.0784430
$945$	−5.33879	−0.173671
$946$	13.6961	0.445297
$947$	−35.0525	−1.13905	−0.569527	−	0.821973i	$-0.692874\pi$
$947$	−35.0525	−1.13905	−0.569527	+	0.821973i	$0.692874\pi$
$948$	−3.72454	−0.120968
$949$	−4.62914	−0.150268
$950$	5.38654	0.174763
$951$	−17.5178	−0.568055
$952$	−1.53832	−0.0498571
$953$	−48.1635	−1.56017	−0.780085	−	0.625674i	$-0.784824\pi$
$953$	−48.1635	−1.56017	−0.780085	+	0.625674i	$0.784824\pi$
$954$	16.2976	0.527656
$955$	−24.4322	−0.790608
$956$	0.157681	0.00509978
$957$	45.3734	1.46671
$958$	19.9474	0.644472
$959$	3.57402	0.115411
$960$	1.13078	0.0364958
$961$	80.3995	2.59353
$962$	−61.1251	−1.97075
$963$	−6.60840	−0.212953
$964$	3.73674	0.120352
$965$	−4.92166	−0.158434
$966$	−6.06390	−0.195103
$967$	51.8697	1.66802	0.834009	−	0.551751i	$-0.186040\pi$
$967$	51.8697	1.66802	0.834009	+	0.551751i	$0.186040\pi$
$968$	12.6549	0.406743
$969$	9.36988	0.301004
$970$	−1.00000	−0.0321081
$971$	−36.4356	−1.16928	−0.584638	−	0.811294i	$-0.698763\pi$
$971$	−36.4356	−1.16928	−0.584638	+	0.811294i	$0.698763\pi$
$972$	−15.0292	−0.482062
$973$	21.0541	0.674963
$974$	11.9989	0.384469
$975$	−6.96440	−0.223039
$976$	3.51447	0.112496
$977$	−50.9200	−1.62907	−0.814537	−	0.580112i	$-0.803009\pi$
$977$	−50.9200	−1.62907	−0.814537	+	0.580112i	$0.803009\pi$
$978$	−27.2152	−0.870246
$979$	17.3360	0.554060
$980$	−1.00000	−0.0319438
$981$	4.37709	0.139750
$982$	22.1958	0.708297
$983$	−38.8680	−1.23970	−0.619848	−	0.784722i	$-0.712806\pi$
$983$	−38.8680	−1.23970	−0.619848	+	0.784722i	$0.712806\pi$
$984$	3.81890	0.121742
$985$	−8.52752	−0.271710
$986$	−12.6914	−0.404175
$987$	3.39680	0.108121
$988$	33.1753	1.05545
$989$	−15.1011	−0.480187
$990$	−8.37194	−0.266078
$991$	−4.04461	−0.128481	−0.0642406	−	0.997934i	$-0.520463\pi$
$991$	−4.04461	−0.128481	−0.0642406	+	0.997934i	$0.520463\pi$
$992$	−10.5546	−0.335109
$993$	−10.3617	−0.328818
$994$	12.5950	0.399489
$995$	−14.2077	−0.450414
$996$	−13.6971	−0.434010
$997$	8.76418	0.277564	0.138782	−	0.990323i	$-0.455681\pi$
$997$	8.76418	0.277564	0.138782	+	0.990323i	$0.455681\pi$
$998$	−14.8988	−0.471612
$999$	−52.9856	−1.67639

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6790.2.a.bd.1.5	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6790.2.a.bd.1.5	✓	15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6790 = 2 \cdot 5 \cdot 7 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6790.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.13078 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.13078 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.72134 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.13078 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.13078 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.72134 q^{9} -1.00000 q^{10} -4.86363 q^{11} -1.13078 q^{12} +6.15893 q^{13} +1.00000 q^{14} +1.13078 q^{15} +1.00000 q^{16} -1.53832 q^{17} -1.72134 q^{18} +5.38654 q^{19} -1.00000 q^{20} -1.13078 q^{21} -4.86363 q^{22} +5.36258 q^{23} -1.13078 q^{24} +1.00000 q^{25} +6.15893 q^{26} +5.33879 q^{27} +1.00000 q^{28} +8.25016 q^{29} +1.13078 q^{30} -10.5546 q^{31} +1.00000 q^{32} +5.49970 q^{33} -1.53832 q^{34} -1.00000 q^{35} -1.72134 q^{36} -9.92463 q^{37} +5.38654 q^{38} -6.96440 q^{39} -1.00000 q^{40} -3.37723 q^{41} -1.13078 q^{42} -2.81602 q^{43} -4.86363 q^{44} +1.72134 q^{45} +5.36258 q^{46} -3.00394 q^{47} -1.13078 q^{48} +1.00000 q^{49} +1.00000 q^{50} +1.73950 q^{51} +6.15893 q^{52} -9.46802 q^{53} +5.33879 q^{54} +4.86363 q^{55} +1.00000 q^{56} -6.09100 q^{57} +8.25016 q^{58} +2.41013 q^{59} +1.13078 q^{60} +3.51447 q^{61} -10.5546 q^{62} -1.72134 q^{63} +1.00000 q^{64} -6.15893 q^{65} +5.49970 q^{66} -5.72405 q^{67} -1.53832 q^{68} -6.06390 q^{69} -1.00000 q^{70} +12.5950 q^{71} -1.72134 q^{72} -0.751614 q^{73} -9.92463 q^{74} -1.13078 q^{75} +5.38654 q^{76} -4.86363 q^{77} -6.96440 q^{78} +3.29378 q^{79} -1.00000 q^{80} -0.872994 q^{81} -3.37723 q^{82} +12.1130 q^{83} -1.13078 q^{84} +1.53832 q^{85} -2.81602 q^{86} -9.32912 q^{87} -4.86363 q^{88} -3.56441 q^{89} +1.72134 q^{90} +6.15893 q^{91} +5.36258 q^{92} +11.9349 q^{93} -3.00394 q^{94} -5.38654 q^{95} -1.13078 q^{96} +1.00000 q^{97} +1.00000 q^{98} +8.37194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 2 q^{3} + 15 q^{4} - 15 q^{5} + 2 q^{6} + 15 q^{7} + 15 q^{8} + 25 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 + 2 * q^3 + 15 * q^4 - 15 * q^5 + 2 * q^6 + 15 * q^7 + 15 * q^8 + 25 * q^9	\( 15 q + 15 q^{2} + 2 q^{3} + 15 q^{4} - 15 q^{5} + 2 q^{6} + 15 q^{7} + 15 q^{8} + 25 q^{9} - 15 q^{10} + 13 q^{11} + 2 q^{12} + 3 q^{13} + 15 q^{14} - 2 q^{15} + 15 q^{16} + 11 q^{17} + 25 q^{18} + 4 q^{19} - 15 q^{20} + 2 q^{21} + 13 q^{22} + 21 q^{23} + 2 q^{24} + 15 q^{25} + 3 q^{26} + 8 q^{27} + 15 q^{28} + 18 q^{29} - 2 q^{30} + 4 q^{31} + 15 q^{32} + 5 q^{33} + 11 q^{34} - 15 q^{35} + 25 q^{36} + 16 q^{37} + 4 q^{38} + 12 q^{39} - 15 q^{40} + 3 q^{41} + 2 q^{42} + 17 q^{43} + 13 q^{44} - 25 q^{45} + 21 q^{46} + 4 q^{47} + 2 q^{48} + 15 q^{49} + 15 q^{50} + 17 q^{51} + 3 q^{52} + 30 q^{53} + 8 q^{54} - 13 q^{55} + 15 q^{56} + 10 q^{57} + 18 q^{58} + 10 q^{59} - 2 q^{60} - 5 q^{61} + 4 q^{62} + 25 q^{63} + 15 q^{64} - 3 q^{65} + 5 q^{66} + 25 q^{67} + 11 q^{68} - 26 q^{69} - 15 q^{70} + 44 q^{71} + 25 q^{72} + 11 q^{73} + 16 q^{74} + 2 q^{75} + 4 q^{76} + 13 q^{77} + 12 q^{78} + 3 q^{79} - 15 q^{80} + 63 q^{81} + 3 q^{82} + 4 q^{83} + 2 q^{84} - 11 q^{85} + 17 q^{86} - 6 q^{87} + 13 q^{88} + q^{89} - 25 q^{90} + 3 q^{91} + 21 q^{92} + 16 q^{93} + 4 q^{94} - 4 q^{95} + 2 q^{96} + 15 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 2 * q^3 + 15 * q^4 - 15 * q^5 + 2 * q^6 + 15 * q^7 + 15 * q^8 + 25 * q^9 - 15 * q^10 + 13 * q^11 + 2 * q^12 + 3 * q^13 + 15 * q^14 - 2 * q^15 + 15 * q^16 + 11 * q^17 + 25 * q^18 + 4 * q^19 - 15 * q^20 + 2 * q^21 + 13 * q^22 + 21 * q^23 + 2 * q^24 + 15 * q^25 + 3 * q^26 + 8 * q^27 + 15 * q^28 + 18 * q^29 - 2 * q^30 + 4 * q^31 + 15 * q^32 + 5 * q^33 + 11 * q^34 - 15 * q^35 + 25 * q^36 + 16 * q^37 + 4 * q^38 + 12 * q^39 - 15 * q^40 + 3 * q^41 + 2 * q^42 + 17 * q^43 + 13 * q^44 - 25 * q^45 + 21 * q^46 + 4 * q^47 + 2 * q^48 + 15 * q^49 + 15 * q^50 + 17 * q^51 + 3 * q^52 + 30 * q^53 + 8 * q^54 - 13 * q^55 + 15 * q^56 + 10 * q^57 + 18 * q^58 + 10 * q^59 - 2 * q^60 - 5 * q^61 + 4 * q^62 + 25 * q^63 + 15 * q^64 - 3 * q^65 + 5 * q^66 + 25 * q^67 + 11 * q^68 - 26 * q^69 - 15 * q^70 + 44 * q^71 + 25 * q^72 + 11 * q^73 + 16 * q^74 + 2 * q^75 + 4 * q^76 + 13 * q^77 + 12 * q^78 + 3 * q^79 - 15 * q^80 + 63 * q^81 + 3 * q^82 + 4 * q^83 + 2 * q^84 - 11 * q^85 + 17 * q^86 - 6 * q^87 + 13 * q^88 + q^89 - 25 * q^90 + 3 * q^91 + 21 * q^92 + 16 * q^93 + 4 * q^94 - 4 * q^95 + 2 * q^96 + 15 * q^97 + 15 * q^98 - 5 * q^99

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